Estimate of the gradient of a solution of the Dirichlet problem for Monge-Ampère type equations in a domain with nonsmooth boundary

DOI10.1007/BF02364865zbMath0863.35043MaRDI QIDQ1920682

S. I. Prokof'eva

Publication date: 3 June 1997

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

viscosity solutionMonge-Ampère type equation

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) A priori estimates in context of PDEs (35B45) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

Cites Work

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• A priori bounds and necessary conditions for solvability of prescribed curvature equations
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• The Dirichlet problem for the prescribed curvature equations
• SOLUTION OF THE DIRICHLET PROBLEM FOR SOME EQUATIONS OF MONGE-AMPÈRE TYPE
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• ON THE FIRST BOUNDARY VALUE PROBLEM FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces

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